US 3668068 A
Loss of plasma from the loss regions of a static magnetic field confinement system is reduced by localizing in the loss region a radio frequency electromagnetic radiation which is nearly but not exactly in resonance with the ion cyclotron frequency and is arranged to reflect back into the confined plasma ions moving out of the static magnetic field through the loss regions.
Description (OCR text may contain errors)
O Unlted States Patent 1151 3,668,068 Watson 1 51 June 6, 1972 54] PLASMA CONFINEMENT APPARATUS 3,117,912 1/1964 lmhofi et 31.. 176 7 x 3,120,476 2/1964 Post ...176/7 X  Inventor: Christopher John Hamilton Watson, Mer- 3i20470 2,1964 Xmhoff et a1" M176 x ton College, Oxford. England 3,160,566 12/1964 Dana] et a1 176/7 3,170,841 2/1965 Post 176/7 X  Ass1gnee. Emtzd Kglgdloncilktomic Energy Authority, 3.257383 6/1966 Hambergerm .176 X 3,425,902 2/1969 Consoli et a1 ..176/7  Filed: Jan. 21, 1969 Primary Examiner-Reuben Epstein PP'- 792,573 Attorney-Larson,Tay1or&Hinds  n Foreign Application Priority/Peta ABSTRACT V V 7 May 22, 1968 Great Bntam ..24,456/68 Loss of plasma from the loss regions ofa Static magnetic field confinement system is reduced by localizing in the loss region  U.S.Cl ..176/7, 315/111 a radio frequency electromagnetic radiation which is nearly  '3" CL 1/ 00 but not exactly in resonance with the ion cyclotron frequency  F leld of Search ..176/7 and is arranged to reflect back into the confined plasma ions moving out of the static magnetic field through the loss re-  References Cited gions.
UNITED STATES PATENTS 1 Claims, 1 Drawing Figure 3,090,737 5/1963 Swartz ..176/7 X PLASMA CONFINEMENT APPARATUS BACKGROUND OF THE INVENTION The invention relates to plasma confinement apparatus.
For the generation of thermonuclear power, for example, it is necessary to devise means for confining a hot plasma of thermonuclear fuel without the plasma coming into contact with material boundaries. Apparatus designed for containing plasma in this way is also aimed at providing a system of containment that consumes less power than can be secured from thermonuclear reactions taking place within the contained plasma.
Proposals for the containment of plasmas have principally relied upon forming static magnetic fields which reflect escaping ions back into a volume of plasma encompassed by the magnetic fields. Unfortunately, the properties of magnetic fields apparently prohibit the formation of a perfect magnetic confinement system which entirely prevents the loss of plasma particles.
One form of apparatus known as the magnetic mirror machine employs a magnetic field the effect of which is similar to a bottle with an opening at each end. The effective size of the openings is reduced as far as possible in the hope that the rate of loss of plasma through the openings can be reduced to a tolerable level.
A logical development of the mirror machine is the toroidal arrangement in which the magnetic bottle is curved round and joined end to end. This has the disadvantage that the magnetic field decreases with increasing radius so that the contained torus of plasma tends to expand.
It has also been proposed to supplement the magnetic field with radio frequency electromagnetic fields which exert an inward, pressure on the plasma. At least for combining with machines of the magnetic mirror type, it can be shown that the frequency of the electromagnetic field has to be greater than the ion cyclotron frequency and the most promising results ap pear likely with an electromagnetic containment field frequency between the ion cyclotron frequency and the electron cyclotron frequency. However, this arrangement requires such large radio frequency power input as to fail by a factor of more than 2 in the requirement for producing a positive power balance in a thermonuclear reactor.
Exploitation of the ion cyclotron resonance by employing a radio frequency electromagnetic field in exact resonance with the ion cyclotron frequency has also been proposed. However, here again it can be shown that the technique fails to have prospects of securing a positive power balance in a thermonuclear reactor.
This failure of ion cyclotron resonance systems is a consequence of the irreversible transfer of energy from the radio frequency electromagnetic field to the plasma, which is a necessary feature of the system.
The appreciation on which the present invention is based is that with radio frequency fields which are nearly but not exactly in resonance with the ion cyclotron frequency there is a substantially smaller transfer of energy to the plasma as compared with the transfer of energy to the plasma with elec tromagnetic fields in exact resonance with the ion cyclotron frequency. On a single particle model such nearly resonant fields lead to a reversible increase in the transverse energy of the ions as they approach the resonance, but this energy is returned to the radio frequency field as the particle leaves the resonance zone, after being reflected by the magnetic field gradient.
SUMMARY OF THE INVENTION According to the present invention there is provided a plasma confinement apparatus comprising a vessel for containing a gas at low pressure, means for forming in or introducing into the vessel a plasma, means for forming a static magnetic field for confining the plasma, the field being such that lines of force leaving the containing vessel pass through one or more predetermined regions, and means for localising in the said regions radio frequency electromagnetic radiation which is nearly but not exactly in resonance with the ion cyclotron frequency and is arranged to reflect or to tend to reflect back into the confined plasma ions moving out of the static magnetic field through the said regions.
Analysis of the equations of motion of a single ion particle in a combined static magnetic field and R.F. electromagnetic field nearly resonant with the ion cyclotron frequency has yielded adiabatic invariants of the motion which are local functions of the RF. field strength. This means that the components of the particle velocity in directions parallel and perpendicular to the magnetic field approximately return to their original magnitudes when the particle orbit returns to a point from which it set out. In particular, a particle which leaves the center of a mirror machine, moves into a region of strong,
even near-resonant, RF. field and then returns to its starting point gains virtually no energy in the process. This is the vital property of near resonance systems. It is perhaps rather surprising, since it seems to imply some automatic adjustment of the phase of the particle in its near resonant motion. It is a consequence of the fact that under adiabatic conditions, the phase dependent term in the equation of energy transfer is oscillatory in time and hence readily separable from the phase independent term.
Specific arrangements embodying the invention will now be described by way of example and with reference to the accompanying drawing which is a highly diagrammatic sectional illustration of a magnetic mirror machine.
DESCRIPTION OF SPECIFIC EMBODIMENTS The machine comprises a vacuum vessel 11 at each end of which is a cavity resonator 12, 13. Each cavity 12, 13 has an aperture communicating with the interior of the vacuum vessel ll. R.F. electromagnetic power for the cavities is supplied along transmission lines l4, 15 from an R.F. power source 16.
Coils l7, 18 are supplied with direct electric current for setting up the static magnetic mirror field indicated by field lines 19.
While a simple magnetic mirror machine has been described, it will be appreciated that, in practice, a machine of the minimum B type would be preferred. In the simple magnetic mirror machine described, the magnetic field decreases radially from the center. In a minimum B type of machine, the field is arranged to have a minimum at the center. This is achieved, for example, in the magnetic well machine by coils arranged with their planes perpendicular to the planes of the mirror field coils and carrying currents in opposed senses so as to generate a quadrupole field superimposed on the magnetic mirror field. The axis of rotation of the quadrupole field is perpendicular to the axis of rotation of the mirror field.
A specific example of a mirror machine embodying the invention has a peak mirror field of the order of 200 kilogauss. Circularly polarised R.F. standing waves are set up at each of the two loss regions of the magnetic field, the frequency to being slightly greater than the peak value of ion cyclotron frequency 0. For deuterium at 200 kilogauss the cyclotron frequency is around 10 Hertz. The field strength required to contain a thermonuclear ion, say a keV deuteron, is not unreasonable. The electric field strength E required for this may be shown to be E =4.5.l0-" /3 volts per centimetre which is comparable with fields used in linear accelerators.
The radiation pressure associated with such field strengths is of the order of 1/ 10 (w O.)/w atmospheres and it has to be established that such radiation could be maintained in the presence of plasma at several atmospheres pressure. However it is believed that a substantial fraction of the plasma pressure may be transferred onto the static magnetic field.
In other examples embodying the invention near resonant R.F. fields are employed to supplement the magnetic field in high-[3 plasma magnetic field systems such as the thetatron or cusp. (The ,8 of the system being the ratio of the kinetic pressure of the plasma to the magnetic field pressure.)
The significance of the high-B assumption is that one cannot set any lower limit to the magnetic field within the plasma, and consequently there is no obvious lower limit to the size of the hole through which a magnetic surface enclosing the plasma can be made to pass. Furthermore, since such systems are inherently non adiabatic, one cannot in general make any predictions about the size of the hole through which particles can escape. In the case when the field has axial symmetry, however, it may be shown that one can use the constancy of the energy and canonical angular momentum to calculate the particle losses through the line and spindle regions of a cusp, assuming that no electric fields develop to hinder those losses. One concludes that both losses are equal, and are equivalent to free flow through holes of area (3/2) m-"' R r, where R is the maximum plasma radius and r, is the minimum ion Larmor radius at the cusp. The hole size in the thetatron may be of the same order. On this basis, a long thetatron would appear marginally more favorable. Assuming that no more is required of the RF. field than to close, by radiation pressure, two holes of this size, the surface area over which radiation pressure must act is now smaller than the maximum plasma cross section by a factor of order of r, /R, whereas in a mirror machine the corresponding factor was l/R,, the reciprocal mirror ratio. Thus a significant reduction in the R.F. power requirement may be obtained with the thetatron as compared with the mirror machine. For example, if as before we take the peak magnetic field to be 200 KG, for which the Larmor radius of a keV tritium ion is approximately 0.4 cm, we obtain an improvement in RF. pressure requirement over the corresponding low-B mirror machine amounting to a factor of around 20.
It will be appreciated that one may not necessarily be concerned, or able, to eliminate the loss of plasma from the loss regions of the static magnetic field by the near resonant electromagnetic radiation field technique described. However, the technique is advantageous in reducing the loss of plasma from these loss regions.
1. Plasma confinement apparatus comprising a vesel for containing a gas at low pressure, means for forming in or introducing into the vessel a plasma, means for forming a static magnetic field for confining the plasma, which magnetic field has one or more loss regions defined as the regions within which the lines of force of the magnetic field leave the containing vessel, and means for localizing in the said regions radio frequency electromagnetic radiation, the frequency of which is greater than the peak ion cyclotron frequency and near to but not exactly in resonance with the ion cyclotron frequency, the said electromagnetic radiation being operative to reflect or to tend to reflect back into the confined plasma ions moving out of the static magnetic field through the said regions.